We will be using Carnigie Learning for the school year on 2022-2023
Throughout Grade 6, students reason, look for structure, and identify similarities across mathematical domains: number and operations, proportionality, expressions, equations and relationships, measurement and data, and personal financial literacy. Composing and Decomposing begins this work by deepening student understanding of numbers and shapes and exploring their relationships. Students compose familiar numbers and shapes into less familiar or more complicated ones. They decompose large numbers and complex shapes into smaller numbers and simpler shapes to perform calculations. As students become more flexible with how they see shapes and numbers, they will better understand their structure, which in turn will enable them to develop strategies for solving problems across mathematical domains. Students learn to approach a problem by decomposing (taking apart) or composing (putting together) objects or numbers already understood. By grade 6, students have developed some number sense; they have broken down numbers into sums, differences, products, and quotients. Now, students discover that numbers are composed of numerical expressions, and learn to make use of the distributive property. In previous grades, students studied basic shapes and determined their areas. Now, they calculate the area of complex shapes by composing them from familiar shapes. Students have studied whole numbers, fractions, and decimals. Now, they learn to see these forms of numbers as composing a single set that can all be plotted on the same number line. Module 1 sets the stage for the habits of mind students will develop as they grow in their mathematical understanding. To see structure across domains, students must be able to shift perspective and see objects and numbers as entities on which to operate, not just as isolated objects or numbers. When students encounter a new idea, they should ask themselves, “Is this problem or idea similar to another problem or idea I’ve learned in the past?” “Are there similarities between this topic and a previously learned topic?”